Related papers: A short proof of the irreflexivity conjecture

We give a one-sentence proof of McLaughlin and Rundell's inverse uniqueness theorem.

We give a brief proof of a recent result of Avron, Seiler and Simon.

These are the lecture notes from a five-hour mini-course given at the Winter School on Galois Theory held at the University of Luxembourg in February 2012. Their aim is to give an overview of Serre's modularity conjecture and of its proof…

In this short note we give counterexamples to several results related to extension theorems published recently.

We prove existence of conjugate Galois representations, and we use it to derive a simple method of weight reduction. As a consequence, an alternative proof of the level 1 case of Serre's conjecture follows.

L. Weinstein's brilliant short proof of de Branges's Theorem is made even shorter by using computer algebra.

(Maher 2012) introduced an approach for relative expressiveness of defeasible logics, and two notions of relative expressiveness were investigated. Using the first of these definitions of relative expressiveness, we show that all the…

We prove several extensions of the Erdos-Fuchs theorem.

We demonstrate the existence of a "L\'evy system" for the excursions of a one-dimensional diffusion process above its past-minimum process. As applications we provide a direct proof of D. Williams' decomposition (in both a global and a…

A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)

We develop a topological approach to prove the generalized Lax conjecture using the fact that determinants of sufficiently big symmetric linear pencils are able to express the rigidly convex sets of RZ polynomials of any degree $d$.…

We present a direct proof of the second conjecture made by M. Atiyah and P. Sutcliffe for the case of convex quadrilaterals. Unlike previous work on this conjecture, our proof does not require any computer aided computations. The new proof…

We give a new proof of a theorem of B.M. Bredihin which was originally proved by extending Linnik's solution, via his dispersion method, of a problem of Hardy and Littlewood.

We provide an alternative and self contained proof of the main result of Bennett, Carbery, Tao regarding the multilinear restriction estimate. The approach is inspired by the recent result of Guth about the Kakeya version of multilinear…

This article re-examines Lawvere's abstract, category-theoretic proof of the fixed-point theorem whose contrapositive is a `universal' diagonal argument. The main result is that the necessary axioms for both the fixed-point theorem and the…

We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.

The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only…

The better title is "Yet another FALSE proof of the 4-colour theorem." Please consider all versions of this paper as historical material on the way to a non-computer proof of the 4-colour theorem. Interpreted as proofs, all versions are…

We give a short proof of Chevalley's theorem that every algebraic group is an extension of an Abelian variety by a linear algebraic group. Along the way we treat Bertini's irreducibility theorem.

The purpose of this article is to present my new proof of the the construction and the convergence theorem of spectral sequences of filtered complexes, which is much shorter and cleaner than the "standard" proof.